Solve sqrt{8}+sqrt{50}-sqrt{48}+sqrt{12}

$$\sqrt { 8 } + \sqrt { 50 } - \sqrt { 48 } + \sqrt { 12 }$$

Evaluate

$$7\sqrt{2}-2\sqrt{3}\approx 6.435393321$$

Solution Steps

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$2\sqrt{2}+\sqrt{50}-\sqrt{48}+\sqrt{12}$$

Factor 50=5^{2}\times 2. Rewrite the square root of the product \sqrt{5^{2}\times 2} as the product of square roots \sqrt{5^{2}}\sqrt{2}. Take the square root of 5^{2}.

$$2\sqrt{2}+5\sqrt{2}-\sqrt{48}+\sqrt{12}$$

Combine 2\sqrt{2} and 5\sqrt{2} to get 7\sqrt{2}.

$$7\sqrt{2}-\sqrt{48}+\sqrt{12}$$

Factor 48=4^{2}\times 3. Rewrite the square root of the product \sqrt{4^{2}\times 3} as the product of square roots \sqrt{4^{2}}\sqrt{3}. Take the square root of 4^{2}.

$$7\sqrt{2}-4\sqrt{3}+\sqrt{12}$$

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

$$7\sqrt{2}-4\sqrt{3}+2\sqrt{3}$$

Combine -4\sqrt{3} and 2\sqrt{3} to get -2\sqrt{3}.

$$7\sqrt{2}-2\sqrt{3}$$